MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 387 
—— 7°70739, Mean height = 118°271 centims., 
Ps = — 2°38064, Standard deviation = 2°77622, 
Pe OZR FAO! Yo for normal curve = 314:99, 
B= -0123784, By = 3°235045. 
Thus 28, — 38, — 6 is positive, and the curve is again of Type LV. 
We have 
= 35606; Skewness = ‘04885, 
r = 30:8023, m = 16°4011, 
v= 4°56967, a = 14:9917, 
Yo = 235°323, 
or, for the equation to the curve :— 
x = 14'9917 tan 6, 
yh 235'°323 Co0g22'80234 (Satis 
the axis of x being positive towards dwarfs and the origin 2:2241 on the positive side 
of the centroid-vertical. 
The maximum ordinate = 324°18 and occurs at « = — 20884. 
The curve of Type 1V., together with the normal curve, is drawn (Plate 10, fig. 7). 
If we attempt to fit a curve of Type III., we find p about 322°14, and the range 
limited on the dwarf side at about 99°812 centims. from the mean, or at a height of 
about 18°5 centims. The largeness of p causes this curve to coincide with the normal 
curve to the scale of our diagram. The areal deviations are for the curve of Type IV. 
and for the normal curve 6°1 and 8°3 centims., giving percentage mean errors of 5°56 
and 7°66 in the ordinates respectively. The advantage is again on the side of the 
generalised curve. It will be seen at once that the normal curve by no means well 
represents the number of girls of giant height. The theoretical probability that 
these giants should occur is small, and their actual redundancy over the numbers 
indicated by the normal curve suggests some peculiarity in this direction ; it is fully 
met by the curve of Type 1V. The asymmetry of the curves given by anthropo- 
metrical measurements on children has been noted both by Bowprrcu* and PorTER,*t 
but in their published papers, to which I have had access, they do not give their 
raw material, only the ogive curve arising from Gatrton’s method of percentiles. 
Unfortunately, theoretical evaluation of the skewness of anthropometric statistics 
can only be applied or verified when we have raw material, and not integral frequency 
height and probable deviation, as given by Mr. Porrer, are 118°36 and 3:698. The latter is obtained 
from the mean deviation, but I do not know how the former is to be accounted for. 
* ‘Growth of Children, studied by Gauron’s Method of Percentiles.’ Boston, 1891, p. 496. 
+ ‘Growth of St. Louis Children.’ St. Louis, 1894, p. 299. 
33 apy 2 
